Simulation of condensed phase quantum dynamical system is one of the most challenging topics in theoretical chemistry. Due to the exponential scaling of the computational demand with the system size, standard basis set approaches are impossible for condensed phase quantum systems. On the other hand, Feynman's path integral formulation does not have such numerical issues, and it is now well established that path integral simulation serves as an excellent means for studying time independent equilibrium quantum properties. How to extend such success to the realm of dynamics has attracted significant amount of theoretical effort. A method called path integral centroid dynamics is one of such approaches with great promise. During my graduate research, I worked on rigorous formulation of the path integral centroid dynamics and derivation of approximate methods. Recently, I extended this formulation for nonequilibrium situations. Efforts will continue to employ this new formulation to devise more accurate algorithms of quantum dynamics simulation for general purposes.